Coulomb integrals and conformal blocks in the AdS3-WZNW model - Iguri, Sergio Manuel (2009)
We study spectral flow preserving four-point correlation functions in the AdS3- WZNW model  using the Coulomb gas method on the sphere. We present a multiple integral realization of the  conformal blocks and explicitly compute amplitudes involving operators with quantized values of  the sum of their spins, i.e., requiring an integer number of screening charges of the first kind. The  result is given as a sum over the independent configurations of screening contours yielding a  monodromy invariant expansion in powers of the worldsheet moduli. We then examine the  factorization limit and show that the leading terms in the sum can be identified, in the semiclassical  limit, with products of spectral flow conserving three-point functions. These terms can be rewritten  as the m-basis version of the integral expression obtained by J. Teschner from a postulate for the  operator product expansion of normalizable states in the H+3 -WZNW model. Finally, we  determine the equivalence between the factorizations of a particular set of four-point functions into products of two three-point functions either preserving or violating spectral flow number  conservation. Based on this analysis we argue that the expression for the amplitude as an integral  over the spin of the intermediate operators holds beyond the semiclassical regime, thus  corroborating that spectral flow conserving correlators in the AdS3-WZNW model are related by  analytic continuation to correlation functions in the H+3 -WZNW model.